For the pot roast: Position an oven rack in the center of the oven and preheat to 300 degrees F.
Liberally sprinkle the entire roast with salt and pepper. Heat the vegetable oil in a Dutch oven over medium-high heat. Brown the roast on all sides until golden and caramelized, 5 to 7 minutes per side; reduce the heat if the fat begins to smoke. Transfer the roast to a plate and reduce the heat to medium.
Add the onions and a pinch of salt and saute, stirring occasionally, until just beginning to brown, 8 to 10 minutes. Add the Italian seasoning, crushed red pepper and garlic and saute until fragrant, another minute. Deglaze with the red wine, scraping up the browned bits from the bottom of the pot. Simmer until reduced by about half, another 2 to 5 minutes. Add the stock and thyme and bring to a simmer. Adjust the seasoning of the liquid.
Put the roast back in the pot with any accumulated juices and place in the oven, covered. Cook the roast, turning every 30 minutes and uncovering the pot for the last 30 minutes of cooking, until very tender, 3 to 3 1/2 hours. Transfer the roast to a cutting board and tent with foil. Increase the oven temperature to 350 degrees F for the peppers and bread.
For the sweet peppers: Toss the pepper strips with the olive oil, granulated garlic and some salt and pepper on a baking sheet. Bake, stirring halfway through, until lighter in color and softened, about 45 minutes.
Strain the pot roast jus through a fine-mesh strainer into a bowl and return to the pot. Bring to a simmer and simmer until reduced slightly, 5 to 10 minutes. Adjust the seasoning if necessary. Keep warm.
Once the meat has cooled a bit, remove the twine. Pull the meat into smaller chunks and return to the reduced jus until ready to build the sandwiches.
For the sandwich build: Rub the rolls with some of the giardiniera oil and toast in the oven until golden brown and crispy, 5 to 8 minutes.
Place some beef on a roll, then some sweet peppers (with some of the oil they were cooked in), followed by some hot giardiniera. Pour a small dish of reduced jus. Quickly dunk the whole sandwich in the hot jus, then wrap in deli paper or parchment paper and wait for 2 to 3 minutes while the magic happens. Repeat with the remaining rolls and toppings. When ready, open up and eat!